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                               =1^3


                                                                     1a
1


    1b
=2^1


       2a
2


    2b
=2^2


       3a
4


    3b
=2^3


       4a
8


    4b
=2^4


       5a
16


     5b
=2^5


       6a
32


     6b
=2^6


       7a
64


     7b
=2^7


       8a
128


      8b
=2^8


       9a
256


      9b
=2^9


       10a
512


      10b
=2^10


        11a
1,024


        11b
=3*3


       12a
9


    12b
=3*4


       13a
12


     13b
=3*5


       14a
15


     14b
=3*6


       15a
18


     15b
=3*8


       16a
24


     16b
=3*9


       17a
27


     17b
=3*10


        18a
30


     18b
=3*11


        19a
33


     19b
=3*12


        20a
36


     20b
=3*13


        21a
39


     21b
=3*14


        22a
42


     22b
=3*15


        23a
45


     23b
=3*16


        24a
48


     24b
=3*17


        25a
51


     25b
=3*18


        26a
54


     26b
=3*19


        27a
57


     27b
=3*20


        28a
60


     28b
=3^1


       29a
3


    29b
=3^2


       30a
9


    30b
=3^3


       31a
27


     31b
=3^4


       32a
81


     32b
=3^5


       33a
243


      33b
=3^6


       34a
729


      34b
=4*4


       35a
16


     35b
=4*5


       36a
20


     36b
=4*6


       37a
24


     37b
=4*7


       38a
28


     38b
=4*8


       39a
32


     39b
=4*9


       40a
36


     40b
=4*10


        41a
40


     41b
=4*11


        42a
44


     42b
=4*12


        43a
48


     43b
=4*13


        44a
52


     44b
=4*14


        45a
56


     45b
=4*15


        46a
60


     46b
=4*16


        47a
64


     47b
=4*17


        48a
68


     48b
=4*18


        49a
72


     49b
=4*19


        50a
76


     50b
=4*20


        51a
80


     51b
=4^1


       52a
4


    52b
=4^2


       53a
16


     53b
=4^3


       54a
64


     54b
=4^4


       55a
256


      55b
=4^5


       56a
1,024


        56b
=4^6


       57a
4,096


        57b
=5*5


       58a
25


     58b
=5*6


       59a
30


     59b
=5*7


       60a
35


     60b
=5*8


       61a
40


     61b
=5*9


       62a
45


     62b
=5*10


        63a
50


     63b
=5*11


        64a
55


     64b
=5*12


        65a
60


     65b
=5*13


        66a
65


     66b
=5*14


        67a
70


     67b
=5*15


        68a
75


     68b
=5*16


        69a
80


     69b
=5*17


        70a
85


     70b
=5*18


        71a
90


     71b
=5*19


        72a
95


     72b
=5*20


        73a
100


      73b
=5^1


       74a
5


    74b
=5^2


       75a
25


     75b
=5^3


       76a
125


      76b
=5^4


       77a
625


      77b
=5^5


       78a
3,125


        78b
=6*6


       79a
36


     79b
=6*7


       80a
42


     80b
=6*8


       81a
48


     81b
=6*9


       82a
54


     82b
=6*10


        83a
60


     83b
=6*11


        84a
66


     84b
=6*12


        85a
72


     85b
=6*13


        86a
78


     86b
=6*14


        87a
84


     87b
=6*15


        88a
90


     88b
=6*16


        89a
96


     89b
=6*17


        90a
102


      90b
=6*18


        91a
108


      91b
=6*19


        92a
114


      92b
=6*20


        93a
120


      93b
=6^1


       94a
6


    94b
=6^2


       95a
36


     95b
=6^3


       96a
216


      96b
=6^4


       97a
1,296


        97b
=6^5


       98a
7,776


        98b
=6^6


       99a
46,656


         99b
=7*7


       100a
49


     100b
=7*8


       101a
56


     101b
=7*9


       102a
63


     102b
=7*10


        103a
70


     103b
=7*11


        104a
77


     104b
=7*12


        105a
84


     105b
=7*13


        106a
91


     106b
=7*14


        107a
98


     107b
=7*15


        108a
105


      108b
=7*16


        109a
112


      109b
=7*17


        110a
119


      110b
=7*18


        111a
126


      111b
=7*19


        112a
133


      112b
=7*20


        113a
140


      113b
=7^1


       114a
7


    114b
=7^2


       115a
49


     115b
=7^3


       116a
343


      116b
=7^4


       117a
2,401


        117b
=8*8


       118a
64


     118b
=8*9


       119a
72


     119b
=8*10


        120a
80


     120b
=8*11


        121a
88


     121b
=8*12


        122a
96


     122b
=8*13


        123a
104


      123b
=8*14


        124a
112


      124b
=8*15


        125a
120


      125b
=8*16


        126a
128


      126b
=8*17


        127a
136


      127b
=8*18


        128a
144


      128b
=8*19


        129a
152


      129b
=8*20


        130a
160


      130b
=8^1


       131a
8


    131b
=8^2


       132a
64


     132b
=8^3


       133a
512


      133b
=8^4


       134a
4,096


        134b
=9*9


       135a
81


     135b
=9*10


        136a
90


     136b
=9*11


        137a
99


     137b
=9*12


        138a
108


      138b
=9*13


        139a
117


      139b
=9*14


        140a
126


      140b
=9*15


        141a
135


      141b
=9*16


        142a
144


      142b
=9*17


        143a
153


      143b
=9*18


        144a
162


      144b
=9*19


        145a
171


      145b
=9*20


        146a
180


      146b
=9^1


       147a
9


    147b
=9^2


       148a
81


     148b
=9^3


       149a
729


      149b
=9^4


       150a
6,561


        150b
=9^5


       151a
59,049


         151b
=10^1


        152a
10


     152b
=10^2


        153a
100


      153b
=10^3


        154a
1,000


        154b
=10^4


        155a
10,000


         155b
=10^5


        156a
100,000


          156b
=10^6


        157a
1,000,000


            157b
=10^7


        158a
10,000,000


             158b
=10^8


        159a
100,000,000


              159b
=10^9


        160a
1,000,000,000


                160b
=10^10


         161a
10,000,000,000


                 161b
=11*11


         162a
121


      162b
=11*12


         163a
132


      163b
=11*13


         164a
143


      164b
=11*14


         165a
154


      165b
=11*15


         166a
165


      166b
=11*16


         167a
176


      167b
=11*17


         168a
187


      168b
=11*18


         169a
198


      169b
=11*19


         170a
209


      170b
=11*20


         171a
220


      171b
=11^2


        172a
121


      172b
=12*12


         173a
144


      173b
=12*13


         174a
156


      174b
=12*14


         175a
168


      175b
=12*15


         176a
180


      176b
=12*16


         177a
192


      177b
=12*17


         178a
204


      178b
=12*18


         179a
216


      179b
=12*19


         180a
228


      180b
=12*20


         181a
240


      181b
=13*13


         182a
169


      182b
=13*14


         183a
182


      183b
=13*15


         184a
195


      184b
=13*16


         185a
208


      185b
=13*17


         186a
221


      186b
=13*18


         187a
234


      187b
=13*19


         188a
247


      188b
=13*20


         189a
260


      189b
=14*14


         190a
196


      190b
=14*15


         191a
210


      191b
=14*16


         192a
224


      192b
=14*17


         193a
238


      193b
=14*18


         194a
252


      194b
=14*19


         195a
266


      195b
=14*20


         196a
280


      196b
=15*15


         197a
225


      197b
=15*16


         198a
240


      198b
=15*17


         199a
255


      199b
=15*18


         200a
270


      200b
=15*19


         201a
285


      201b
=15*20


         202a
300


      202b
=15^2


        203a
225


      203b
=16*16


         204a
256


      204b
=16*17


         205a
272


      205b
=16*18


         206a
288


      206b
=16*19


         207a
304


      207b
=16*20


         208a
320


      208b
=17*17


         209a
289


      209b
=17*18


         210a
306


      210b
=17*19


         211a
323


      211b
=17*20


         212a
340


      212b
=18*18


         213a
324


      213b
=18*19


         214a
342


      214b
=18*20


         215a
360


      215b
=19*19


         216a
361


      216b
=19*20


         217a
380


      217b
=20*20


         218a
400


      218b
=20^2


        219a
400


      219b
=25^2


        220a
625


      220b
0/1 =


        221a
0 (any fraction with 0 on
         top is 0)

                            221b
4/0 =


        222a
Undefined


            222b
8^(1/3)


          223a
2


    223b
27^(1/3)


           224a
3


    224b
30:60:90 Right Triangle
      (Lenghts)

                          225a
x:x^(1/3):2x


               225b
64^(1/3)


           226a
4


    226b
125^(1/3)


            227a
5


    227b
216^(1/3)


            228a
6


    228b
343^(1/3)


            229a
7


    229b
512^(1/3)


            230a
8


    230b
729^(1/3)


            231a
9


    231b
Adding and Subtracting
      Decimals

                         232a
Line up the decimal points
   and proceed as usual

                         232b
Adding or subtracting
fractions with different
     denominators
                           233a
Multiply both fractions to
get a common denominator
  add or subtract as usual
                         233b
Adding or subtracting
fractions with the same
      denominator
                          234a
Add or subtract the
numbers on top and keep
 the same denominator
                          234b
Another way to write cube
         root 5

                        235a
5^(1/3)


          235b
Any number to the 0 power
          is?

                        236a
one (1)


          236b
Any number to the first
      power is?

                          237a
itself


         237b
Any number to the negative
  power (y) is equal to?

                        238a
The reciprocal of the same
 number to the positive
  power (y). (eg 3^-2 =
      1/(3^2) = 1/9)
                         238b
Area of a circle?


                    239a
pr^2


       239b
Area of a parallelogram?


                           240a
Base * Height


                240b
Area of a triangle?


                      241a
(b*h)/2


          241b
Basic probability formula?


                         242a
number of outcomes you
 want/total number of
  possible outcomes
                         242b
Circumference of a circle?


                         243a
2pr


      243b
Combinations: single
source, order doesn't
       matter
                        244a
Start with the number of
permutations, that is the
numerator(top). The
Denominator is the number
of combinations (eg 432*1)
                         244b
Distance Formula?


                    245a
Rate * Time = Distance
 (Hint: Draw a chart)

                         245b
Distributing Exponents


                         246a
When several #s are inside
parenthesis, the exponent
outside the parentheses must be
distributed to all the #s within
(4y)^2 = ((4)^2)((y)^2) =
(4^2) * (y^2) = 16y^2            246b
Dividing Decimals


                    247a
Move the decimal to the
  right on both numbers
until there is nothing to the
    right of the decimal
                           247b
Dividing Fractions


                     248a
Invert (reciprocal) the
 second fraction and
       multiply
                          248b
Does (x^2 + y^2 +
z^2)/(x^2 + y^2) = z^2?

                          249a
NO


     249b
Does x^2 + x^3 = x^5?


                        250a
NO


     250b
Does x^6 - x^2 = x^4?


                        251a
NO


     251b
Equation for a line?


                       252a
y=mx+b where b is the y-
intercept (the point which
crosses the y-axis) m is the
slope of the line, and x & y are
the coordinates of some point
on that line                       252b
even + even =


                253a
even


       253b
even + odd =


               254a
odd


      254b
even x even =


                255a
even


       255b
even x odd =


               256a
even


       256b
Exponents - Dividing
numbers with same base

                         257a
subtract the bottom
exponents from the top
exponents (3^6 / 3^2 =
         3^4)
                         257b
Exponents - Multiplying
numbers with same base

                          258a
add their exponents (6^2
      *6^3 = 6^5)

                           258b
Exponents - Raising a
  power to a power

                        259a
Multiply the exponents
(4^3)^2 = 4^(3*2) = 4^6

                      259b
Factor x^2-2xy+y^2


                     260a
(x-y)^2


          260b
Factor x^2-y^2


                 261a
(x+y)(x-y)


             261b
Factor x^2+2xy+y^2


                     262a
(x+y)^2


          262b
How do you find the
 median of a set of
    numbers?
                      263a
arrainge #s from least to
  greatest and take the
  middle number or the
average of the two middle
            #s
                        263b
How do you find the mode
  of a set of numbers?

                       264a
Pick the # that occurs most
         frequently

                          264b
how do you find the range
  of a set of numbers?

                        265a
subtract the smallest
number from the greatest
        number
                       265b
How do you find the slope
       of a line?

                        266a
Difference in the y-
coordinates over the
 difference in the x
     coodinates
                        266b
How do you tell if it's a
  permutation or
   combination?
                            267a
Permutations ask for
  "arraingements"
Combinations ask for
      "Groups"
                       267b
How do you unfactor a
 quadratic equation?
     (x+2)(x+5)
                        268a
FOIL X^2+7x+10


                 268b
If you raise a negative
number to an even power,
   what happens to the
         number?
                        269a
It becomes positive


                      269b
If you raise a negative
number to an odd power,
  what happens to the
        number?
                           270a
It gets smaller


                  270b
If you raise a positive
fraction that is less than 1
to a power, what happens
       to the fraction?
                           271a
It gets smaller


                  271b
Key to percent
increase/decrease

                    272a
amount of
increase/original amount =
x/100 (Then cross multiply
         to find x)
                         272b
multiplying decimals


                       273a
ignor decimal points and multiply the
two numbers, then count the digits to
the right of the decimal points in the
original numbers and place the
decimal so there are the same
number of digits to the right of the
decimal
                                    273b
Multiplying Fractions


                        274a
Multiply the numerators
and put the product over
   the product of the
     denominators
                           274b
odd + odd =


              275a
even


       275b
odd x odd =


              276a
odd


      276b
Odds that at least one thing
       will happen?

                          277a
Will = 1 - Won't


                   277b
Odds that something
  doesn't happen?

                      278a
Won't = 1 - Will


                   278b
Order of operations


                      279a
PEMDAS (parenthesis,
Exponents, Multiplication,
   Division, Addition,
      Subtraction)
                         279b
Permutations: single
source, order matters

                        280a
Multiply the # of choices
for each of the spots--but
  the number of choices
   keeps getting smaller
                             280b
Permutations: single
source, order matters BUT
    only for a selection
                        281a
Multiply the # of choices for
each of the spots--but the
number of choices keeps
getting smaller, stop when
all the places are taken
                            281b
Probability that A and B
   will both happen?

                           282a
A*B (Multiply both
  probabilities)

                     282b
Probability that A or B will
         happen?

                           283a
A+B (Add both
 probabilities)

                  283b
Problem that asks you to
choose a # of items to fill
specific spots, when each
   spot is filled from a
    different source?
                              284a
Multiply the # of choices
 for each of the spots

                            284b
Pythagorean Triples
    (lengths)?

                      285a
3:4:5 -- 5:12:13 -- 7:24:25


                          285b
Right Isosceles triangle
       (lengths)?

                           286a
Side, Side, Side^2


                     286b
Rules for "Plugging in" for
    cosmic problems

                          287a
1)Pick numbers that make sense for the
variable in the problem 2)Find an answer
using those numbers to get the "target
answer" 3)plug your #s into the answer
choices to see which choice equals the
target answer
                                       287b
Rules for "Plugging in" the
     answer choices

                          288a
1)Start with choice "c" plug that
into the problem to see if it
works 2)If "c" is to small go
larger 3) if "c" is too big try
smaller 4)If you don't know try
them all
                                288b
SQRT 1,000,000


                 289a
1,000


        289b
SQRT 1,024


             290a
32


     290b
SQRT 1,296


             291a
36


     291b
SQRT 2


         292a
1.414213562


              292b
SQRT 2,401


             293a
49


     293b
SQRT 3


         294a
1.732050808


              294b
SQRT 4


         295a
2


    295b
SQRT 4,096


             296a
64


     296b
SQRT 6,561


             297a
81


     297b
SQRT 9


         298a
3


    298b
SQRT 10,000


              299a
100


      299b
SQRT 10,000,000,000


                      300a
100,000


          300b
SQRT 16


          301a
4


    301b
SQRT 25


          302a
5


    302b
SQRT 36


          303a
6


    303b
SQRT 49


          304a
7


    304b
SQRT 64


          305a
8


    305b
SQRT 81


          306a
9


    306b
SQRT 100


           307a
10


     307b
SQRT 100,000,000


                   308a
10,000


         308b
SQRT 121


           309a
11


     309b
SQRT 169


           310a
13


     310b
SQRT 225


           311a
15


     311b
SQRT 256


           312a
16


     312b
SQRT 400


           313a
20


     313b
SQRT 625


           314a
25


     314b
SQRT 729


           315a
27


     315b
The solvability rule


                       316a
You must have at least as
many distinct equations as
   you have variables
                         316b
Two fractions that equal
   each other with one
variable how do you solve
          for x?
                        317a
Cross multiply


                 317b
Unfactor (x-y)^2


                   318a
x^2-2xy+y^2


              318b
Unfactor (x+y)(x-y)


                      319a
x^2-y^2


          319b
Unfactor (x+y)^2


                   320a
x^2+2xy+y^2


              320b
What happens if you
  multiply or divide both
sides of an inequality by a
    negative number?
                          321a
The direction of the
inequality symbol changes

                        321b
What is the difference
between a permutation or a
      combination?
                        322a
Combinations don't care
 about the order of the
       problems
                          322b
When is a number divisible
          by 3?

                         323a
if the sum of its can be
divided evenly by 3 (216, is
because 2+1+6 is divisible
           by 3)
                           323b
When is a number divisible
          by 4?

                         324a
if the number formed by
 it's last 2 digits is divisible
by 4 (3,028 is because 28 is
         divisible by 4)
                              324b
When is a number divisible
          by 6?

                         325a
if it is divisible by both 2
 and 3 (318 is because it is
even and the sum of 3+1+8
       is divisible by 3)
                            325b
Work Problems?


                 326a
simmilar to distance but ...
Think how much of the job
can be done in one hour (as
  a fration of the whole).
                          326b

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